asce structures 2005 final
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STRESS IN ORTHOTROPIC STEEL DECK COMPONENTS DUE TO
VEHICULAR LOADS
WanChun Jen1 and Ben T. Yen2
1ATLSS Research Center, Lehigh University, 117 ATLSS Drive, Bethlehem, PA; PH
(610) 758-5613; FAX (610) 758-6568; email:jew2@lehigh.edu2ATLSS Research Center, Lehigh University, 117 ATLSS Drive, Bethlehem, PA; PH
(610) 758-5553; FAX (610) 758-6568; email:bty0@lehigh.edu
Abstract
Laboratory measurement of local stresses was made on components of a full
scale model of orthotropic deck panel of Bronx-Whitestone Bridge. Simulated wheel
load of trucks was placed on the deck at various locations along longitudinal
stiffening ribs of trapezoidal shape. The loads induced local stresses and local
bending of diaphragm web plates and rib walls. The local stresses were moderately
high in magnitude in all components of the model deck.
Introduction
Orthotropic steel decks with longitudinal, closed rib stiffeners serve the dual
function of being the upper flange of the box girder, real or equivalent, and being the
member to transfer vehicular loads to other parts of the bridges. Stresses induced by
vehicular loads are the primary cause of fatigue cracks in decks. Some analytical and
experimental studies have been conducted to examine the local stresses in deck
components in order to alleviate fatigue cracking at connections between longitudinal
ribs and transverse diaphragms (Connor 2001, Tsakopoulos 2002, Ye 2004).
After the fatigue testing in laboratory of a full scale model deck of the Bronx-
Whitestone Bridge (BWB) in New York City, stresses at various components of the
specimen were measured for examination of the regional effect of wheel loads of
trucks. This paper briefly summarizes some of the results.
Test Specimen and instrumentation
The model deck of BWB was 48 feet (14.63 m) long and 37 feet (11.28 m) wide,
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as shown schematically in Figure 1. It consisted of 2 panels of continuous deck
supported by three floorbeams. The floorbeams were each supported by a wall
column, and by a stiffening girder at the other end, Figure 2. The test deck modeled
half of the bridge width with the test deck plate connected to the wall longitudinally
simulating continuity at the center line of the bridge.
REACTION WALL
16
15
14
13
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10
9
8
7
6
5
4
3
2
1
Diaphragm
A1
Floor
Beam A
Floor
Beam C
Floor
Beam B
Diaphragm
B1
N
LOADIND POSITION
Rib No.
1 2 43
Figure 1 Top View of Specimen Setup
Figure 2 Elevation of Specimen
The orthotropic deck had 5/8 in. (16 mm) thick deck plate, two longitudinal
plate stiffeners and fourteen longitudinal trough stiffeners with 5/16 in. (8 mm) thick
wall. The diaphragm web was inch (13 mm) thick.
2
Line 1
Line 5, 6
...
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The trapezoidal ribs were 13 in. (330 mm) wide at the top, 5 in. (127 mm) wide
at the bottom and the inclined walls were 14 in. (357 mm) deep. The spacing between
ribs is also 13 in. (330 mm), so the deck plate is supported uniformly for most of its
width.
A large number of strain gages and displacement transducers (LVDTS) were
placed between Diaphragm A1 and B1. The emphasis was on measuring strains in the
deck components at Diaphragm B. Figure 3 shows schematically the strain gage
locations around Rib 6 at Diaphragm B.
Loading Procedure
Hydraulic actuators applied vertical loads though rubber pads (footprints) to the
deck to simulate wheel loads of HS 25 trucks. Since linear behavior at details was
observed from strain reading during loading, each applied load was increased from
20K to 80K to exaggerate the strains in the components for easy comparison.
Figure 3 Strain Gage Location and Loading Lines, Rib 6 at Diaphragm B
Figure 4 Loading Positions
The loads were applied individually along six lines, as depicted in Figure 3.
These lines simulate the truck wheels directly over the connections of ribs wall to the
deck plate, and in between.
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Four load positions were used in each line: above Diaphragm A1, halfway
between A1 and B, above Diaphragm B and halfway between B and B1. These
positions are indicated in Figure 4.
Results
Linear Elastic Behavior
The test deck behaved linear elastically under the applied load. Figure 5 shows
as examples the load versus deflection relationship at nine LVDTs throughout the test
deck. The load was on Line 1 at Position 2. Figure 6 shows the load versus strain
relationship of four strain gages at Diaphragm B1. In all cases, the deflection and
strain increased linearly with the applied load, and return to the same original value
when the loads were removed.
Strains in the Deck Pate
The strain distributions on the bottom of deck plate along Diaphragm A1 when
the simulated load was at different positions on Line 6 are plotted in Figure 7. Line 6
was along the mid-width of Rib 8. With 80K applied at Position 1 directly over
Diaphragm A1, the maximum stress on the bottom of the deck at Rib 8 was not the
highest. The highest stress of about 7 Ksi (230 in/in strain) occurred when the load
was at Position 2 between Diaphragm A1 and B. When the 80K load was at Position
4 between two diaphragms, the bottom of the deck plate was in low tension at the
junction with the rib wall at Ribs 8, 9 and 10.
0
20
40
60
80
100
120
-0.05 0 0.05 0.1 0.15 0.2 0.25
Deflection (inch)
Load
(kips)
LVDT_1
LVDT_2
LVDT_3
LVDT_4
LVDT_5
LVDT_6LVDT_7
LVDT_8
LVDT_9
Figure 5 Load vs Deflection (Line 1, Loading Position 2)
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0
200
400
0 20 40 60 80 100 120
Strain ( in./in.)
Load(kips)
Strain Gage 46
Strain Gage 47
Strain Gage 13
Strain Gage 15
Figure 6 Load vs. Strain at Diaphragm B1 (Line 1, Loading Position 2)
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0
50
100
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Distance (inch)
Strain(in./
in.) Loading Position 1 Loading Position 2
Loading Position 3 Loading Position 4
Loading Position 3+4 Loading Position 2+3+4
Figure 7 Strains on the Bottom of Deck Plate along Diaphragm A1 (Loads on Line 6)
Figure 8 shows the strain distribution on the bottom of deck plate along
diaphragm B under the same loading positions of Figure 7. All stresses were low
under a 80K load, with a maximum of less than 10 Ksi (3450 in/in strain) when the
5
P = 80 K
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applied load was between diaphragms. Under a wheel load of HS 25, the maximum
live load stress under the deck would be less than 3 Ksi.
The strain distributions along Diaphragm B in Figure 8 indicate that the regional
influence of loads on deck plate stresses was confined to only the adjacent one or two
ribs.
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0
100
200
300
400
500
600
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Distance (inch)
Strain(in./
in.)
Loading Position 1
Loading Position 2
Loading Position 3
Loading Position 4
Loading Position 3+4
Loading Position 2+3+4
Figure 8 Strains on Bottom of Deck Plate along Diaphragm B (Loads on Line 6)
Stresses in Diaphragm at Cutout
The longitudinal stiffening ribs passed though diaphragm webs at cutouts, as
shown in Figure 2 and 3. The geometry of the cutout was determined by analysis and
was one of the main reasons of fatigue testing the model deck. In the static testing of
the deck model to examine the regional effects of loads, strains on diaphragm webs at
cutouts were measured when loads were applied at various positions. Example results
are presented in Figures 9 to 10.
In Figure 9, the strains on Diaphragm B at the top of cutout for Ribs 6, 7, 8, and
9 are presented. The loads were applied along Line 3 over the connection between the
deck and a web of Rib 6. When the 80K load was at Position 2 between diaphragms,
the highest strain of about 380 in/in was induced at the cutout at the other web of
Rib 6. That is corresponding to less than 3 Ksi under a wheel load of HS 25.
Again, the influence of a wheel load on local stresses is limited to one adjacent
6
P = 80 K
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rib only, as depicted by the strains in Figure 9.
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0
100
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Distance (inch)
ObservedstrainsatCuto
Loading Position 1
Loading Position 2
Loading Position 3
Loading Position 4
Loading Position 3+4
Loading Position 2+3+4
Figure 9 Strains at Cutout on South Face of Diaphragm B (Loads on Line 3)
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0
100
-10 0 10 20 30 40 50 60 70 80 90 100
Distance (inch)
Strains(in./
in.)
Line 1
Line 2
Line 3
Line 4
Line 5
Figure 10 Strains on the South Face of Diaphragm B at Cutout (Loading Position 2)
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P = 80 K
P = 80 K
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The variation of stresses on Diaphragm B at cutouts of Rib 6 to 9 for loading
Position 2 of Loading Line 1 to 5, are presented in Figure 10. Position 2 is between
diaphragms. As the loading line moved away from Rib 6 (to Lines 4 and 5), the
strains at the cutout of Rib 6 decreased. The region of effect of only one adjacent rib
is again obvious. When the applied load was on Line 5 over Rib 8, relatively high
strains developed in Rib 8. There was a connection of the diaphragm between Rib 8
and Rib 9 (as shown in Figure 2), which affected the behavior of Rib 8.
Influence Line of Strains
The strain diagrams presented so far, Figure 7 to 10, provide information on the
distribution of stresses in deck components near the point of loading. The subsequent
diagrams show the magnitude of strain at specific points as a load was applied at
different locations nearby. The results are essentially Influence Lines.
Figure 11 shows the horizontal and vertical strains on the web of Diaphragm B
at the connection of deck plate and Rib 6. The strain gage locations are given in
Figure 3. Both the horizontal and vertical strains (at gage 10x and 12y) were highest
when the 80K load was directly above. The magnitude of strains at these gages
decreased as the load was placed away. Similarly, the horizontal and vertical strains
at gage 20(x) and 22(y) were the highest when the load was directly above. When the
load was at Line 5 over Rib 7, the strain at all four gages at Rib 6 were near zero.
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0
100
200
300
400
0 5 10 15 20 25 30 35 40 45 50
Loading Line Distance (inch)
Strain(
in./
in.)
Gage 10 x
Gage 20 x
Gage 12 y
Gage 22 y
Figure 11 Influence Lines of Horizontal (x) and Vertical (y) Strains on Diaphragm B
at Connection of Deck and Rib 6 (Loading Position 2)
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Line 1 2 3 4 5
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0
200
400
600
0 5 10 15 20 25 30 35 40 45 50
Loading Line Distance (inch)
Strain
(i
n./
in.)
Gage 128 N
Gage 129 S
Gage 134 N
Gage 135 S
Figure 12 Influence Lines of Strains on North and South Faces of Diaphragm B at
Top of Cutout, Rib 6 (Loading Position 2)
On Diaphragm B at the cutout of Rib 6, strains on the South surface of the
diaphragm web at the top of cutout (Figure 12) were slightly higher when the load
was at Line 2 between the rib walls than when the load was directly over the walls.
The difference in strains at back to back strain gages (128/129,134/135) indicates that
the diaphragm web was subjected to local bending. In this case, the magnitude of
bending was about the same on the two sides of Rib 6. On the other hand, the
diaphragm web plate local bending was not prominent at the lower corners of the
cutout, as the strains at back to back strain gages (130/131, and 132/133 in Figure 13)
increased or decreased similarly. All four gages had the highest strain when the
applied load was directly above, and had almost no strain when the load was one rib
away.
The rib walls were also subjected to local bending when the applied load was
nearby. The Influence Lines for strain gage pairs on the walls of Rib 6 are given in
Figure 14. The difference in strain between the gages of each pair (137/138, 139/140)
signifies local plate bending. The maximum difference was about 350 in/in in the
5/16 in. thick plate, comparing to about 400 in/in in the in. web plate of
Diaphragm B in Figure 12.
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Line 1 2 3 4 5
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0
200
400
600
0 5 10 15 20 25 30 35 40 45 50
Loading Line Distance (inch)
Strain(in./
in.)
Gage 130 N
Gage 131 S
Gage 132 N
Gage 133 S
Figure 13 Influence Lines of Strains on Diaphragm B at Lower Corner of Cutout,
Rib 6 (Loading Position 2)
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0
200
400
600
0 5 10 15 20 25 30 35 40 45 50
Loading Line Distance (inch)
Strain(in./
in.)
Gage 137 N
Gage 138 S
Gage 139 N
Gage 140 S
Figure 14 Influence Lines of Strains on Web of Rib 6 (Loading Position 2)
Figure 15 shows the Influence Line of strain on the wall of Rib 6 between
Diaphragm B and B1. When the applied load was at Position 4 directly over the cross
section of the rib, the bottom of the rib had the highest strain whether the load was
over the rib wall or in between. The shape of these Influence Lines is typical for a
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Line 1 2 3 4 5
Line 1 2 3 4 5
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continuous beam. The strains on the web of the rib about an inch from the deck and
directly below the applied load along Line 3, however, decreased without changing
sign when the load was moved away. For this Loading Line, there was practically no
local strain at the point on the opposite web of the rib.
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0
200
400
600
800
1000
1200
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Distance (inch)
Strain(in./
in.)
Rib wall East Line 2
Rib bottom Line 2
Rib wall West Line 2
Rib wall East Line 3
Rib bottom Line 3
Rib wall West Line 3
Figure 15 Influence Lines of Strain on Rib 6 between Diaphragm B and B1
Discussions and Conclusions
The strains in components were measured when a simulated wheel load of trucks
was placed at various locations on the deck. Results indicate that the local stresses
induced by the wheel load were essentially zero when the wheel load was one rib
away in the transverse direction of the orthotropic deck. By considering the
configuration of trucks on the bridge, it can be concluded that wheel loads of parallel
trucks have little effect on the local stresses in deck plate, diaphragms and rib walls.
In the longitudinal direction, multiple simulated wheel loads were applied during
testing. Because of the difference in stiffness of the diaphragms with or without
floorbeams, the effect of load position on local stresses was strongly influence by the
relative position of the loads to the diaphragms. Results of strain measurement
confirmed the linear elastic behavior of the deck and thus the adequacy of
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superposition of multiple loads. Computer analysis using a finite element model also
confirmed the measured strains when one or multiple simulated wheel loads were
applied.
A limited parametric study of the deck component dimensions is being
conducted. Preliminary results indicate that were the deck plate thickness be reduced
to in. with all other thickness and dimensions being the same, the stresses in
diaphragms would increase slightly under the simulated wheel load while the stresses
in the rib walls would increase more. Obviously the relative dimensions of
components have strong effect on local stresses. For the specific replacement
orthotropic deck of BWB, it can be calculated that vehicle induced local stresses in
the components are moderately high but well within permissible values.
Acknowledgments
The funding for this study was from Pennsylvania Infrastructure Technology
Alliance (PITA) and the model deck was provided by Triborough Bridge and Tunnel
Authority of New York City (TBTA). The prototype deck panel was designed by
Weidlinger Associate Inc. of New York City and manufactured by Leonard Kunkin
Associates of Line Lexington, PA. Testing was conducted at ATLSS Research Center
of Lehigh University.
References
Connor, R. J. and Fisher, J. W. (2001), Results of Field Measurements on the
Williamsburg Bridge Orthotropic Deck," ATLSS Report 01-01.
Tsakopoulos, P. T., and Fisher, J. W. (1999), Williamsburg Bridge, Replacement
Orthotropic Deck, As-Built Full-Scale Fatigue Test," ATLSS Report 99-02.
Tsakopoulos, P. T., and Fisher, J. W. (2002), Fatigue Resistance Investigation for
the Orthotropic Deck on the Bronx-Whitestone Bridge," ATLSS Report 02-05.
Ye, Q., and Fanjiang, G. N. (2004). Analysis and Design of Steel Orthotropic
Decks, IABSE, Shanghai, China, Sep. 2004. 222-223
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